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8/23/07
Returns…
•
are percentage changes
•
% change = final – initial/ initial
•
can be negative
Basis point
•
Definition: 1% = 100 basis points
•
65 basis points = 0.65%
Working with percentages
1.) Percentages are not symmetric
a.
Percentages are not parallel
b.
Example: Earn 10% on portfolio, then lose 10% on it, do you break even?
i.
No
c.
$40 stock becomes $50 stock = return of 25%, $50 becomes $40 = return
of 20%; note that we can start and end at $40, but we earn 25% on the
way up and lose 20% on the way down
2.) You don’t add percentage changes
a.
Example: in year 1, earn 25%; in year 2, lose 20%, but notice, answer is
0% as net return (after year 1 & 2)
3.) How to compute returns from other returns?
a.
$40
$50
$40
b.
(25%) (20%)
c.
x
y
z
d.
(30%) (10%)
e.
Return = % change
f.
Factor = 1 + return
g.
Example: Return of 25%
<> Factor of 1.25
i.
Return of 5% <> Factor =1.05
ii.
Return of 200% <> Factor =3
iii.
Return of 20% <> Factor = 0.80
iv.
Using factors:
1.
$40 becomes $50, what is your return?
a.
25%
2.
Suppose you have $1000 invested in a stock that you
purchased at $40, it rises to $50. How much is your
investment worth?
a.
$1250
3.
$40 stock becomes $50, every $1 invested becomes?
a.
$1.25
h.
Example: Earn 30%, then lose 10%
i.
Cumulative return =
ii.
Returns
factors
iii.
30%
1.30
iv.
10%
0.90
v.
Cumulative factor = Factor * factor
i.
= (1.30) (0.90)
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= 1.17
vi.
Cumulative return = 1.171 = 0.17 or 17%
i.
Example: Total cumulative factor = (1 + return1) * (1+return2)
j.
Total cumulative return = TCF – 1
k.
Example: $1 in stock becomes worth $9 in 13 years
i.
Return = 800%
1.
= 91/1 = 8 or 800%
ii.
Return of 100% <> factor = 2
iii.
Return of 200% <> factor = 3
iv.
Return of 400% <> factor = 5
v.
Final/initial – initial/initial
vi.
Factor

1
vii.
Return + 1 = factor
Compounding
•
Earn 10% a year for 30 years, what would be your total cumulative return after 30
years?
•
Every $1 would become $X after 30 years.
•
Total cumulative factor = (1.1)(1.1)(1.1)… (1.1)
•
= 1.1
30
fefe
•
= 17.4494
•
17.4494 – 1 = 16.4494
Reverse compounding or roots
•
Invest $1, it becomes worth $10 in 12 years.
•
What is our annualized return? OR What is our compound return?
•
If we earn X%, then after 12 years, we would have a return of 900%
•
Factor = 10
•
10 = (1+x)(1+x)… (1+x)
•
10 = (1+x)
12
•
12
√
10 = 1+x
annual factor
o
x
√
y = y
1/x
•
1.211528 = Annualized factor
•
21.1528% = Annualized return/compound return
8/28/07
From last time
•
Factors: Total cumulative factor, annual factor
•
Returns: Annual return, monthly return, daily return, total cumulative returns, 5
year total return
•
Annualized return
o
Also known as compound return
o
Geometric average return
o
5year annualized return
o
starting point and ending point & calculate a fixed return that gets you
from point A to point B
o
Smooth return
Constant compound return
It ignores in between returns
Observation:
•
Every return needs two prices
•
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This note was uploaded on 04/15/2008 for the course BNAD 301 taught by Professor Sugiyama during the Fall '07 term at University of Arizona Tucson.
 Fall '07
 Sugiyama

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